scholarly journals Zakharov-Shabat system and hyperbolic pseudoanalytic function theory

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
Viktor G. Kravchenko ◽  
Vladislav V. Kravchenko ◽  
Sébastien Tremblay
Keyword(s):  
Function Theory ◽  
Pseudoanalytic Function

scholarly journals A Regularization Process for Electrical Impedance Equation Employing Pseudoanalytic Function Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Cesar Marco Antonio Robles Gonzalez ◽  
Ariana Guadalupe Bucio Ramirez ◽  
Volodymyr Ponomaryov ◽  
Marco Pedro Ramirez Tachiquin
Keyword(s):  
Inverse Problem ◽  
Taylor Series ◽  
Regularization Method ◽  
Electrical Impedance ◽  
Function Theory ◽  
Forward Problem ◽  
Problem Method ◽  
Pseudoanalytic Function ◽  
Ill Posed

The electrical impedance equation is considered an ill-posed problem where the solution to the forward problem is more easy to achieve than the inverse problem. This work tries to improve convergence in the forward problem method, where the Pseudoanalytic Function Theory by means of the Taylor series in formal powers is used, incorporating a regularization method to make a solution more stable and to obtain better convergence. In addition, we include a comparison between the designed algorithms that perform proposed method with and without a regularization process and the autoadjustment parameter for this regularization process.

scholarly journals First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Marco Pedro Ramirez-Tachiquin ◽  
Cesar Marco Antonio Robles Gonzalez ◽  
Rogelio Adrian Hernandez-Becerril ◽  
Ariana Guadalupe Bucio Ramirez
Keyword(s):  
Electrical Impedance ◽  
Dirichlet Boundary ◽  
Function Theory ◽  
New Method ◽  
Two Dimensional ◽  
Dirichlet Boundary Value Problem ◽  
The Finite Element Method ◽  
Impedance Tomography ◽  
Pseudoanalytic Function

Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary conditions are exact solutions of the electrical impedance equation, performing a brief comparison with the finite element method. Finally, we discuss the possible contributions of these results to the field of the electrical impedance tomography.

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